To ensure the generated response being semantically controlled by DA, the GPT-2 model is continuously pre-trained on large amounts of annotated DA-response pairs \(\mathcal {D}=\lbrace (a_n, y_n)\rbrace _{n=1}^{N}\) , which have been developed in the research community, including the MultiWOZ dataset [1]} and the Frame corpus [2]}.
As illustrated in Figure REF , each training pair is pre-processed into a sequence of tokens by concatenating \(Y\)  and \(a\) , and is fed into GPT-2. Model parameters \(\theta \)  are updated to maximize the log-likelihood of the conditional probability in Equation REF  over training samples:
\(\mathcal {L} (\theta ) = \sum _{n=1}^{|\mathcal {D}|} \sum _{t=1}^{T_n} \log P_r(y_{t,n} | y_{<t,n}, a_n ; \theta )\) 
